# An airplane is at height of 10000 feet. At what angle (rounded to whole degree), it must descend if the airport is 50 miles away?

Mar 25, 2017

Airplane must descend at ${2}^{\circ}$.

#### Explanation:

As one mile is $1760$ yards and each yard $3$ feet, we have $1760 \times 3 = 5280$ feet in a mile and

airport is $5280 \times 50 = 264000$ feet away.

Hence tangent (equal to opposite side divided by adjacent side) of angle formed is $\tan \alpha = \frac{10000}{264000} = 0.03788$

and looking at tables (or scientific calculator) angle $\alpha = {2.17}^{\circ}$, which rounded to degrees is ${2}^{\circ}$.